Evaluate the limit and explain why each student is correct or incorrect

Problem 2: [10 pts] Morgan, Avery, and Taylor are asked to evaluate the limit lim ry2 - 2.x2 (x,y)=(8,4) y4 - 4x2 . . Morgan writes lim cy- - 2x2 (x,y) =(8,4) 14 - 4x2 = and concludes from this that the limit does not exist. . Avery notes that along x = 0, xy2 - 2.x2 0 -0 xy2 - 2x2 0 - 2x2 y4 - 4x2 y4 _ 0 = 0 and that along y = 0, NIH y4 - 4x2 0 - 4.x2 Avery concludes that the limit does not exist since the function tends to different values along different paths. . Taylor notes that along y = mx, ry2 - 2x x(mx)2 - 2.2 max - 2 24 - 4x2 m'x - 2 (mx)4 - 4x2 mix _ 4: " 7 0, and as a -> 0, m4x4 - 4 Taylor concludes that the limit exists and is equal to , Determine which students, if any, provided a correct response. If a student did not provide a correct response, make sure to explain what error (or errors) they made. If none of the students are correct, calculate the limit correctly, or explain why it does not exist